The U.S. Census Bureau reported that the mean area of U.S. homes built in 2012 was 2505 square feet. Assume that a simple random sample of 20 homes built in 2013 had a mean area of 2581 square feet, with a standard deviation of 225 square feet. At a 0.01 significance level test the claim that homes built in 2013 were larger than homes built in 2012.